Surreal number

In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similar to superreal numbers and hyperreal numbers. By limiting the construction to a Grothendieck universe, a set is obtained, rather than a class, with an honest field with the cardinality of some strongly inaccessible cardinal.

Related Topics:
Mathematics - Field - Real numbers - Infinitesimal number - Absolute value - Superreal number - Hyperreal numbers - Grothendieck universe - Set - Obtained - Class - Field - Strongly inaccessible cardinal

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The definition and construction of the surreals is due to John Conway, and exemplifies Conway's characteristic notational cleverness and originality. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first presented in a work of fiction. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had simply called numbers originally. Conway liked the new name, and later adopted it himself. Conway then described the surreal numbers and used them for analyzing games in his 1976 book On Numbers and Games.

Related Topics:
John Conway - Donald Knuth - Pure Mathematics - On Numbers and Games

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